Remark Similar results are provided in Theorem 5 of [1]}, but the authors did not consider pointwise convergence of posterior mean and used concentration function as the proof technique instead. Indeed, our equivalence theory allows one to derive posterior contraction under the \(L_\infty \)  norm based on \(L_\infty \)  convergence rates of \(\hat{f}_n\)  in the KRR literature. For example, under a very similar setting, Corollary 2.1 in [2]} shows that
\(\Vert \hat{f}_n-f_0\Vert _\infty \lesssim \left(\frac{\log n}{n}\right)^{\frac{\alpha }{2\alpha +1}}\) 
